Johnson Solids (Page 5)

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(J86) Sphenocorona
Vertices:  10  ({4 + 2}[4] + {2 * 2}[5])
Faces:14  ({4 * 2 + 2 * 2} equilateral triangles + 2 squares)
Edges:22
Symmetry:  2-fold Pyramidal  (C2v)
(values below based on edge length = 1)
Volume:sqrt(2*(2+3*sqrt(6)    
    +2*sqrt(13+3*sqrt(6))))/4    
≈1.5153516399764065597